What is the integral of 10cos(100x) ?

The integral of 10cos(100x) is 1/10 sin(100x)+C

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integral of 10cos(100x)

\int 10 cos (100 x) d x

\frac{1}{10} sin (100 x) + C

Solution steps

\int 10 cos (100 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int cos (100 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{100} d u

= 10 \cdot \int cos (u) \frac{1}{100} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \frac{1}{100} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 10 \cdot \frac{1}{100} sin (u)

Substitute back

u = 100 x

= 10 \cdot \frac{1}{100} sin (100 x)

Simplify

10 \cdot \frac{1}{100} sin (100 x) : \frac{1}{10} sin (100 x)

= \frac{1}{10} sin (100 x)

Add a constant to the solution

= \frac{1}{10} sin (100 x) + C

\frac{2}{x - 3}

\int \frac{1}{x ^{2} - 8 x + 65} d x

2 x + 1

\int 5^{- 5 x} d x

(x^{9} - 3 x)^{- 2}

What is the integral of 10cos(100x) ?
The integral of 10cos(100x) is 1/10 sin(100x)+C